As Swisher notes, Kleiner is being sued by one of its female partners, Ellen Pao, for gender discrimination, so people are naturally going to notice the hire of another woman.

But that's not the real reason why you should raise your eyebrows at this move.

Tilenius's background is in e-commerce and payments. She ran merchant services at eBay's PayPal unit for years. And then she joined Google, launching Google Wallet—and attracting a lawsuit from eBay, which accused her of misappropriating trade secrets. (Google denied the claim.)

The job of executive in residence is slightly different from the job of entrepreneur in residence. Both are positions in which venture-capital firms place individuals they're interested in working with who don't have a venture to jump into right away. Entrepreneurs in residence generally scout new startup ideas or early-stage companies they can join, while executives in residence typically assume operating roles at portfolio companies. LinkedIn CEO Jeff Weiner was an executive in residence at Greylock before joining the company, for example.

As an executive in residence at Kleiner, Tilenius will help coach companies currently in Kleiner's portfolio, and possibly look for operating roles with one of them. Tilenius "will be focusing on late-stage companies in its $1 billion Digital Growth Fund," Swisher writes.

One of those companies is Square, the mobile-payments startup that's targeting small businesses with its smartphone credit-card reader and elegantly designed apps.

Square COO Keith Rabois is part of the original crew who launched PayPal as a startup and sold it to eBay for $1.5 billion. It is no secret in Silicon Valley that there's no love lost between that crowd and the eBay executives—like Tilenius—who succeeded them after the sale, and in their view, wasted a lot of PayPal's potential.

It's going to get really interesting if Tilenius attempts to focus on Square.

UPDATE: Kleiner Perkins told us that contrary to Swisher's original report, Tilenius's title will be executive in residence, not entrepreneur in residence.